Earthquake-caused Direct Economic Loss Assessment:BP Neural Network And Its Application

As a destructive natural disaster, the earthquake is an enormous threat to people’s life and property.In China where there are vast and huge land and territory, earthquakes that magnitude up above6happen every year. In recent years, the most famous one is the Wenchuan earthquake in Sichuan on May12,2008, which killed and missed more than eighty thousand people, and up to845.1billion RMB yuan of the direct economic loss, brought people endless hurt.After each earthquake, the state government has to respond quickly and judge the earthquake magnitude, the focal depth, the intensity, and other parameters such as the area, casualties and property losses and so on promptly, in order to arrange the following disaster relief and rebuilding work. On one hand, some parameters such as magnitude, disaster area distribution are easy to judge, however, earthquake-caused direct economic loss would need some methods to estimate. Rapid assessment of earthquake-caused direct economic losses is of great significance:First of all, it will affect government arrange disaster recovery and financial investment directly, and will guide the scale of social donations; Secondly, rapid assessment of earthquake-caused direct economic losses can help insurance company to deal with a variety of claims work after the earthquake, to help insurance company improve the subsequent service quality; Finally, as an important tool for catastrophe risk management, catastrophe bonds’ trigger condition is directly related to earthquakes loss, rapid assessment of earthquake-caused direct economic losses constitute a prerequisite for the development of catastrophe bonds.In the second chapter, based on the concept of earthquake-caused direct economic losses, the paper introduces and summarizes some traditional evaluation methods for earthquake-caused direct economic loss, such as vulnerability classification method, investigation, and remote sensing image method. But for these methods, there are some disadvantages in the speed and accuracy. For example, the vulnerability classification method which based on earthquake damage matrix is quick to evaluate and the result is relatively accurate, but highly relies on historical earthquake disaster database; the investigation which based on sampling statistics is more accurate, but needs more survey data, and takes more time and energy, so this method is not suitable for a rapid assessment; Remote sensing image recognition method, although can achieve rapid evaluation, only briefly to the extent of damage of buildings, so the precision to estimate the loss is limited.So we consider introducing BP neural network to assess and measure the earthquake-caused direct economic loss. For there are some discrete and complex nonlinear relationship which is difficult to determine among the trigger factors of earthquake-caused direct economic loss, so it’s very difficult to model directly. However, first of all, the BP neural network which only contains a single hidden layer which has proven in theory can achieve any function approximation at any precision; Secondly, BP neural network don’t need consider too much inherent logic between independent variables and dependent variable, and only need train sufficient typical sample data to get the inner logic and rule, further to get good generalization ability to fit or forecast other samples which are not trained; Besides, large-scale parallel structured neural network can rapidly handle the train process which involves lots of complex operations, greatly shorten the training time and improve the learning ability. After comprehensive consideration, there are some feasibility and advantages to estimate the direct economic losses with BP neural network.This paper then introduces the basic theory of artificial neural network, such as neurons, primary function, activation function and supervised learning, especially discusses the structure of BP network and the traditional gradient descent algorithm in details. However, although the traditional gradient descent algorithm for BP neural network can get a stable solution of weight matrix and threshold vector, there are some shortcomings, such as the BP network can easily fall into the local minimum points, learning process may reverberate, and slow convergence speed. Some of these problems are the BP neural network’s inherent disadvantages, such as local minimum points, but other two problems can be improved through some methods. Then this paper briefly introduces the following 12optimization algorithms:momentum gradient descent algorithm (traingdm), adaptive learning speed gradient descent algorithm (traingda), adaptive learning rate momentum gradient descent algorithm (traingdx), elastic BP algorithm (trainrp), Fletcher-Reeves conjugate gradient algorithm (traincgf), Polak-Ribiers conjugate gradient algorithm (traincgp), Powell-Beale conjugate gradient algorithm (traincgb), normalized conjugate gradient algorithm (trainscg), BFGS quasi-newton algorithm (trainbfg), step segmentation algorithm (trainoss), Levenberg-Marquardt algorithm (trainlm) and Bayesian regularization algorithm (trainbr).Although various optimization algorithms above are superior to traditional gradient descent algorithm in the way of operation speed and preventing shock, BP network still has some obvious flaws. Such as training process maybe trap in some local minimum points, which have to change initial weight values though many training to achieve a global minimum point. In addition there is no effective way to make sure the number of hidden neurons which is also a very important problem, too little hidden neurons may lead to owe fitting that can’t achieve ideal generalization ability; too many hidden neurons may also lead to too long training time and over fitting. So we need to rely on some previous design experience and try many times in order to find suitable numbers of hidden neurons based the accuracy of the target premised, at the same time comprehensive think about other factors such as network structure, the input and output of the number of the element, the difficulty of solving problem.In chapter4, we use some sample data on BP neural network to make empirical analysis to the earthquake-cased direct economic loss. First of all, the paper discusses several factors influenced the earthquake direct economic losses from two aspects of hazard-formative factors and hazard-affected factors, such as magnitude, focal depth, the affected population, disaster area, design basic earthquake acceleration and an estimate of the disaster area GPD, output is earthquake-caused direct economic loss. Then the paper introduces the related data sources, at the same time, in order to improve the neural network training speed we pretreat the data. According to Hornik’s theorem, we chose BP neural network only containing a hidden layer, as to the number of hidden nodes, for there is no conclusion for this problem, so this paper just make a try until get an satisfied result. Besides we try the above12optimization algorithms one by one and consider3to12hidden node number one by one, finally we choose LM algorithm (trainlm) as a training function and six hidden nodes which gets an ideal training result.In order to prevent over fitting and get more excellent generalization ability of neural network, this paper divides all samples into three parts such as training sample, confirm sample, test sample and puts forward an optimized method for initial weights. At last, by writing Matlab order language we get a neural network, and discussed the output result.This paper in the last chapter summarizes the main conclusion, innovation points and the insufficiency, and discusses further research prospect.Based on the risk management and related actuarial theory as the guide, combined theoretical and empirical analysis the paper make a deep discuss on BP neural network applied to earthquake-caused direct economic loss. At the same time, with the qualitative and quantitative research methods, we make a detailed analysis to the BP neural network to evaluate earthquake-caused direct economic loss which has certain practical significance.